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Cited by 16Quantum Mechanics and Non-Hermitian PhysicsQuantum Mechanics and ApplicationsSpectral Theory in Mathematical Physics

Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force

Open access
Gardas, Bartłomiej, Deffner, Sebastian, Saxena, Avadh·2016·Physical Review A
DOI 10.1103/physreva.94.022121
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Abstract

A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external ``observer.'' Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Therefore, even a possibility to describe physical reality by means of non-Hermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. Here, we show that non-Hermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Furthermore, we propose a quantum canonical transformation that maps Hermitian systems onto non-Hermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.

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Crossref · 10.1103/physreva.94.022121

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  • |ρ(∞)〉〉 is a linear combination of those {|ζ_k〉〉} with Re[λ_k]=0.

    “This means that | ρ ( ∞ ) 〉 〉 is a linear combination of those {| ζ k 〉 〉} with Re[ λ k ] = 0 [2, 5, 48].”

    From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [48]

    Section II describes a state as a superposition of Hamiltonian eigenstates and discusses when its evolution is unitary. It does not address a long-time density state |ρ(∞)〉〉 or a decomposition selected by Re[λ_k]=0; searches for those terms and for steady-state Liouvillian eigenvalues found no relevant passage. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

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Research works printed but not linked: 2

  1. X.-M. H. Meng-Jun Hu and Y.-S. Zhang, Are observables necessarily Hermitian?, arXiv:1601.04287. · arXiv
  2. H. Goldstein, C. P. Poole, and J. L. Safko, Classical Mechanics (Addison-Wesley, Reading, MA, 2002).

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Related

Authors
Gardas, B., Deffner, S., & Saxena, A.
Affiliations
Los Alamos National Laboratory (US)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2016-08-26
Volume
94
Issue
2
ISSN
  • 0556-2791 (ISSN-L)
  • 2469-9926
  • 2469-9934
DOI
10.1103/physreva.94.022121
OpenAlex
W2290490295
Cited by
16
References
45
Citations by year
2025: 2 · 2023: 2 · 2022: 2 · 2021: 2 · 2020: 3 · 2018: 1 · 2017: 3 · 2016: 1
FWCI
0.79
Type
journal article
Language
en
Open access
Licence
Locations
  • Physical Review A (publishedVersion, other-oa)
  • arXiv (Cornell University) (submittedVersion)
  • Maryland Shared Open Access Repository (USMAI Consortium) (submittedVersion, public-domain)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
  • arXiv (Cornell University)
  • Digital Repository at the University of Maryland (University of Maryland College Park) (public-domain)
Funders
  • U.S. Department of Energy
  • Los Alamos National Laboratory
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
Keywords
non-Hermitian operators, quantum measurement, repeatability of measurements, non-commuting observables, real spectrum, inertial forces

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